Answer:
θ = ω0 t + 1/2 ω t^2 = 1/2 α t^2 since it starts from rest
α = (15000 / 60) / 240 = 250 / 240 = 1.04 rev/sec^2
Note that α is in rev/sec^2
T(otal) = 1/2 * 1.04 * 240^2 = 30,000 revolutions
Check:
Average RPM = (15000/2) = 7500 rev/min = 125 / sec
125 / sec * 240 sec = 30,000 rev
